RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 1972, Volume 12, Issue 2, Pages 155–156 (Mi mz9862)  

A problem of Ulam

V. V. Ermakov

M. V. Lomonosov Moscow State University

Abstract: Let $R$ be a set of positive integers with usual operations of addition and multiplication
$$ a+b=s(a,b);\quad a\cdot b=m(a,b);\quad a,b\in R. $$
A correspondence is set up between each one-to-one (Peano) mapping $p$ of the space $R\times R$ onto the whole of $R$ and the two functions
$$ \begin{aligned} \sigma(c)&=\sigma[p(a,b)]=s(a,b);
\mu(c)&=\mu[p(a,b)]=m(a,b). \end{aligned} $$
It is proved in this note that there can be no Peano mapping for which $\sigma(\mu(c))=\mu(\sigma(c))$ for all $c$ in $R$.

Full text: PDF file (185 kB)

English version:
Mathematical Notes, 1972, 12:2, 528–529

Bibliographic databases:

UDC: 511.2
Received: 18.11.1971

Citation: V. V. Ermakov, “A problem of Ulam”, Mat. Zametki, 12:2 (1972), 155–156; Math. Notes, 12:2 (1972), 528–529

Citation in format AMSBIB
\Bibitem{Erm72}
\by V.~V.~Ermakov
\paper A problem of Ulam
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 2
\pages 155--156
\mathnet{http://mi.mathnet.ru/mz9862}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=314625}
\zmath{https://zbmath.org/?q=an:0243.04002}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 2
\pages 528--529
\crossref{https://doi.org/10.1007/BF01095011}


Linking options:
  • http://mi.mathnet.ru/eng/mz9862
  • http://mi.mathnet.ru/eng/mz/v12/i2/p155

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Математические заметки Mathematical Notes
    Number of views:
    This page:83
    Full text:41
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020